Abstract

In this study, we derive a comprehensive forward model for the data collected by stripmap synthetic aperture radar (SAR) that is linear in the ground reflectivity parameters. It is also shown that if the noise model is additive, then the forward model fits into the linear statistical model framework, and the ground reflectivity parameters can be estimated by statistical methods. We derive the maximum likelihood (ML) estimates for the ground reflectivity parameters in the case of additive white Gaussian noise. Furthermore, we show that obtaining the ML estimates of the ground reflectivity requires two steps. The first step amounts to a cross-correlation of the data with a model of the data acquisition parameters, and it is shown that this step has essentially the same processing as the so-called convolution back-projection algorithm. The second step is a complete system inversion that is capable of mitigating the sidelobes of the spatially variant impulse responses remaining after the correlation processing. We also state the Cramer-Rao lower bound (CRLB) for the ML ground reflectivity estimates.We show that the CRLB is linked to the SAR system parameters, the flight path of the SAR sensor, and the image reconstruction grid.We demonstrate the ML image formation andmore » the CRLB bound for synthetically generated data.« less

@article{osti_1347353,
title = {Inverse problems-based maximum likelihood estimation of ground reflectivity for selected regions of interest from stripmap SAR data [Regularized maximum likelihood estimation of ground reflectivity from stripmap SAR data]},
author = {West, R. Derek and Gunther, Jacob H. and Moon, Todd K.},
abstractNote = {In this study, we derive a comprehensive forward model for the data collected by stripmap synthetic aperture radar (SAR) that is linear in the ground reflectivity parameters. It is also shown that if the noise model is additive, then the forward model fits into the linear statistical model framework, and the ground reflectivity parameters can be estimated by statistical methods. We derive the maximum likelihood (ML) estimates for the ground reflectivity parameters in the case of additive white Gaussian noise. Furthermore, we show that obtaining the ML estimates of the ground reflectivity requires two steps. The first step amounts to a cross-correlation of the data with a model of the data acquisition parameters, and it is shown that this step has essentially the same processing as the so-called convolution back-projection algorithm. The second step is a complete system inversion that is capable of mitigating the sidelobes of the spatially variant impulse responses remaining after the correlation processing. We also state the Cramer-Rao lower bound (CRLB) for the ML ground reflectivity estimates.We show that the CRLB is linked to the SAR system parameters, the flight path of the SAR sensor, and the image reconstruction grid.We demonstrate the ML image formation and the CRLB bound for synthetically generated data.},
doi = {10.1109/taes.2016.140519},
journal = {IEEE Transactions on Aerospace and Electronics Systems},
number = 6,
volume = 52,
place = {United States},
year = 2016,
month =
}

The maximum likelihood (ML) method for regression analyses of left-censored data is improved for general acceptance by considering the censored observations to be doubly censored. The existence of a lower bound (i.e., the concentration of a pollutant cannot be negative) is included; the improved ML method utilizes this information in the formulation of a likelihood function. The improved ML method has been translated into an equivalent least squares (LS) method, and an iterative algorithm is presented to estimate the statistical parameters from this LS translation. The LS translation is easy to explain to nonstatisticians, and computational requirements for implementing themore » LS method are minimal. The methodology is applied to a mechanistic model for air transport and deposition of polycyclic aromatic hydrocarbons (PAH) to a snow surface. For a censored data set, parameter estimates of the model, namely, dry deposition velocities and washout ratios, were obtained for various PAH species by using the following three procedures: (1) the NAG-15 routine for maximization of a likelihood function; (2) the proposed algorithm for the equivalent LS method; and (3) the modified iterative least squares method.« less

This paper presents an evaluation of the performance of the maximum likelihood (ML) method when used to determine simulation data for generators from standstill frequency response (SSFR) tests. The generator or synchronous machine data found by this process or similar processes are used in simulation models for many kinds of stability and dynamic performance calculations. The robustness of the ML method is demonstrated by analyses made with SSFR data from tests on the Rockport 722 MVA generator. It is shown that a unique set of parameters can be obtained and the noise effects can be dealt with effectively when themore » Maximum Likelihood estimation (ML) technique is used to estimate machine parameters.« less